What Is the Geometric Interpretation of the Derivative of a Velocity Vector?

[Seedling]

Hi,

I'm trying to get a geometric idea of what the derivative of a velocity vector is. For example if you're talking about the space between vx and vx + dvx, where vx is a velocity along the x axis.

Would it be like an infinitesimal sphere around the end of the vector?

Thanks...

(Added thought: I guess it doesn't matter if it's a velocity vector or some other kind of vector...shouldn't have been so specific).

 

[HallsofIvy]

Why would you want a geometric idea of something that is not geometric? The derivative of the velocity vector is the acceleration vector! That's the best way of thinking about it.

As for "some other kind of vector", a "vector" doesn't have a derivative, a vector function does. If you think of the vector function itself as being the "position vector" of a point moving along a curve, the derivative points along the tangent to the curve and its length is the speed of the point.

 

[near]

by the language of calculus, the derivative of a velocity vector is simply the second derivative of the length from which the the velocity vectoar was derived or in simple means, it,s the accelaration vector already. and this accelaration vector can be split into its components the tangential and radial acceleration (this is for a curve surface).